Complex dependency structures are often conditionally modeled, where random effects parameters are used to specify the natural heterogeneity in the population. When interest is focused on the dependency structure, inferences can be made from a complex covariance matrix using a marginal modeling approach. In this marginal modeling framework, testing covariance parameters is not a boundary proble...

Neyman-Pearson or frequentist inference and Bayes inference are most clearly differentiated by their approaches to point null hypothesis testing. With very large samples, the frequentist and Bayesian conclusions from a classical test of significance for a point null hypothesis can be contradictory, with a small frequentist P -value casting serious doubt on the null hypothesis, but a large Bayes...

This document provides example R code demonstrating how to use the BayesSingleSub package (Section 1), and the technical details for the sampling routines (Section 2). 1 Tutorial for computing de Vries and Morey's Bayes factors Here, we show how to compute the Bayes factors B ar , B trend , B int , and B t+i , and how to obtain and plot the posterior distributions of the model parameters. First...

Relative surprise regions are shown to minimize, among Bayesian credible regions, the prior probability of covering a false value from the prior. Such regions are also shown to be unbiased in the sense that the prior probability of covering a false value is bounded above by the prior probability of covering the true value. Relative surprise regions are shown to maximize both the Bayes factor in...

A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering the largest value attained so far by such a martingale, the exaggeration will be limited, and there are systematic ways to eliminate it. The inverse of the ...

In this paper we derive global Bayes factors for the comparison of a parametric model with a nonparametric alternative. The alternative is constructed by embedding the para-metric model in a mixture of Dirichlet Processes. Results include a general explicit form for partially exchangeable sequences as well as closed form expressions in the context one-way analysis of variance. Our results raise...

Starting from the Näıve Bayes model, we develop a new concept for aggregating items of evidence in classification problems. We show that in Näıve Bayes, each feature variable contributes a multiplicative adjustment factor to the estimated class probability. We next introduce a way of controlling the importance of the feature variables by raising each adjustment factor to a different power. The ...